The length of base of triangle must be greater than 6 cm
Solution:
Let "b" be the base of triangle
Let "a" and "c" be the two sides of triangle
Given that one side is 2 cm shorter than the base
one side = 2 cm shorter than base
a = b - 2 ---- eqn 1
Also given that other side is 3 cm longer than the base
other side = 3 cm longer than the base
c = 3 + b ---- eqn 2
The perimeter of triangle is given as:
P = a + b + c ---- eqn 3
Given that perimeter is greater than 19 cm
P > 19
Substitute eqn 1 and eqn 2 in eqn 3
b - 2 + b + 3 + b > 19
3b + 1 > 19
3b > 19 - 1
3b > 18
Divide both sides by 3
b > 6
Thus length of base of triangle must be b > 6 cm